Nonsquare Spectral Factorization for Nonlinear Control Systems

This paper considers nonsquare spectral factorization of nonlinear input affine state space systems in continuous time. More specifically, we obtain a parametrization of nonsquare spectral factors in terms of invariant Lagrangian submanifolds and associated solutions of Hamilton–Jacobi inequalities. This inequality is a nonlinear analogue of the bounded real lemma and the control algebraic Riccati inequality. By way of an application, we discuss an alternative characterization of minimum and maximum phase spectral factors and introduce the notion of a rigid nonlinear system.

Stewarding Privilege: Transitioning to Millennial Leadership in Christian Family Foundations

While Christian family philanthropy has significant potential to influence the viability and success of Christian ministry, it is an understudied area of investigation. In surveying its context, both formal and informal structures provide the framework for stewarding this privilege. These are under pressure to change due to generational shifts, family dynamics, evolving expressions of faith, and shifts in philanthropy itself. These pressures create specific challenges for the leadership of foundations by descendants of the Christian founders as they grapple with donor intent, ongoing stewardship, daily operations, and public accountability by their foundations. Succession is a common transition for organizational life that is also experienced within Christian family foundations. Though studies on family philanthropy succession are few, research pertinent to family business succession can be applied to the topic. As new generations inherit the responsibility of continuing the founders’ legacy, common failures in the succession process reveal roadblocks for smooth transitions. One must create the conditions for a smooth transition to next generation leadership in Christian family philanthropy. Following the self-emptying surrender of Christ, founders must be prepared to take a leap of faith and release control. Descendants must learn confidence and self-differentiation strategies that permit them to acquire their own vision for stewarding family philanthropy. For each person, trust in God\u27s guidance is required. To facilitate a successful transition for next generation leaders, an experiential nine-month philanthropy incubator has been designed. This artifact assists next generation philanthropists to learn together with their peers through giving and volunteering with charitable projects. By learning as a community of practice through participation in small projects together with non-profit practitioners, they gain confidence, knowledge, perspective, and vital tools for future leadership in generosity. The program will serve eight givers and eight non-profit leaders in the first year. The artifact will define recruitment strategies, project selection criteria, budget, program content, methodology, retreat specifications, personnel needs (mentors, retreat facilitators), workflow, timetable, and evaluation processes. The dissertation has narrowly focused on stewarding the privilege of next generation Christian family philanthropy. Additional areas for further investigation are suggested, along with a consideration of the drivers behind the current research

Sea-floor tectonics and submarine hydrothermal systems

The discovery of metal-depositing hot springs on the sea floor, and especially their link to chemosynthetic life, was among the most compelling and significant scientific advances of the twentieth century. More than 300 sites of hydrothermal activity and sea-floor mineralization are known on the ocean floor. About 100 of these are sites of high-temperature venting and polymetallic sulfide deposits. They occur at mid-ocean ridges (65%), in back-arc basins (22%), and on submarine volcanic arcs (12%). Although high-temperature, 350°C, black smoker vents are the most recognizable features of sea-floor hydrothermal activity, a wide range of different styles of mineralization has been found. Different volcanic substrates, including mid-ocean ridge basalt, ultramafic intrusive rocks, and more evolved volcanic suites in both oceanic and continental crust, as well as temperature-dependent solubility controls, account for the main geochemical associations found in the deposits. Although end-member hydrothermal fluids mainly originate in the deep volcanic basement, the presence of sediments and other substrates can have a large effect on the compositions of the vent fluids. In arc and backarc settings, vent fluid compositions are broadly similar to those at mid-ocean ridges, but the arc magmas also supply a number of components to the hydrothermal fluids. The majority of known black smoker vents occur on fast-spreading mid-ocean ridges, but the largest massive sulfide deposits are located at intermediate- and slow-spreading centers, at ridge-axis volcanoes, in deep backarc basins, and in sedimented rifts adjacent to continental margins. The range of deposit sizes in these settings is similar to that of ancient volcanic-associated massive sulfide (VMS) deposits. Detailed mapping, and in some cases drilling, indicates that a number of deposits contain 1 to 5 million tons (Mt) of massive sulfide (e.g., TAG hydrothermal field on the Mid-Atlantic Ridge, deposits of the Galapagos Rift, and at 13°N on the East Pacific Rise). Two sediment-hosted deposits, at Middle Valley on the Juan de Fuca Ridge and in the Atlantis II Deep of the Red Sea, are much larger (up to 15 and 90 Mt, respectively). In the western Pacific, high-temperature hydrothermal systems occur mainly at intraoceanic back-arc spreading centers (e.g., Lau basin, North Fiji basin, Mariana trough) and in arc-related rifts at continental margins (e.g., Okinawa trough). In contrast to the mid-ocean ridges, convergent margin settings are characterized by a range of different crustal thicknesses and compositions, variable heat flow regimes, and diverse magma types. These variations result in major differences in the compositions and isotopic systematics of the hydrothermal fluids and the mineralogy and bulk compositions of the associated mineral deposits. Intraoceanic back-arc basin spreading centers host black smoker vents that, for the most part, are very similar to those on the mid-ocean ridges. However, isotopic data from both the volcanic rocks and the sulfide deposits highlight the importance of subduction recycling in the origin of the magmas and hydrothermal fluids. Back-arc rifts in continental margin settings are typically sediment-filled basins, which derive their sediment load from the adjacent continental shelf. This has an insulating effect that enhances the high heat flow associated with rifting of the continental crust and also helps to preserve the contained sulfide deposits. Large hydrothermal systems have developed where initial rifting of continental crust or locally thickened arc crust has formed large calderalike sea-floor depressions, similar to those that contained major VMS-forming systems in the geologic record. Hydrothermal vents also occur in the summit calderas of submarine volcanoes at the volcanic fronts of arcs. However, this contrasts with the interpreted settings of most ancient VMS deposits, which are considered to have formed mainly during arc rifting. Hydrothermal vents associated with arc volcanoes show clear evidence of the direct input of magmatic volatiles, similar to magmatic-hydrothermal systems in subaerial volcanic arcs. Several compelling examples of submarine epithermal-style mineralization, including gold-base metal veins, have been found on submarine arc volcanoes,and this type of mineralization may be more common than is presently recognized. Mapping and sampling of the sea floor has dramatically improved geodynamic models of different submarine volcanic and tectonic settings and has helped to establish a framework for the characterization of many similar ancient terranes. Deposits forming at convergent margins are considered to be the closest analogs of ancient VMS. However, black smokers on the mid-ocean ridges continue to provide critically important information about metal transport and deposition in sea-floor hydrothermal systems of all types. Ongoing sea-floor exploration in other settings is providing clues to the diversity of mineral deposit types that occur in different environments and the conditions that are favorable for their formation

Doctor of Philosophy

dissertationBryostatin 1 is a highly complex marine natural product originally isolated by Pettit in the 1960s. Since its structural elucidation in 1982 bryostatin 1 has attracted considerable attention for the treatment of several human diseases such as cancer, HIV, and Alzheimer's. Bryostatin 1 exerts it effect by binding to and activating Protein Kinase C (PKC) isozymes with nanomolar affinity. Bryostatin 1 is unique among the many known activators in that it is nontumor promoting. Contrastingly, the Phorbal ester PMA, which shares the same binding pocket, is one of the most potent tumor promoters known. Despite intense medical interest, the development of bryostatin 1 as a therapeutic has been impeded by its extremely low natural abundance. To address this problem numerous groups have developed elegant syntheses of the natural bryostatins. Another and perhaps more attractive solution however is the synthesis of simplified bryostatin analogues. Towards this end the Keck group synthesized the analogue Merle 23, which in cell assays demonstrated either a PMA like response or a bryostatin like response depending on the cell line. This paradoxical behavior illustrates the complexity of PKC activation as therapeutic strategy, and Merle 23 provides a valuable tool for probing the subtle differences between tumor promoting and nontumor promoting PKC ligands. Described within is the scaled synthesis of Merle 23 and it use for further probing the biological consequence of PKC activation at the transcriptional level. Merle 23 as well as two less lipophilic analogues Merle 35 and Merle 37 are also shown to be potent activators of latent HIV reservoirs. Central to the Keck group's analogue work is identifying strategies by which the synthetic burden can be reduced. In order to simplify the synthesis of new analogues the use of simple aromatic building blocks as surrogates for the A and B ring pyrans was explored. Using phenyl rings to replace the pyrans resulted in an analogue that failed to maintain high affinity binding in spite of it still containing all of the elements previously believed to be responsible for binding

AUTOMATED CYBER OPERATIONS MISSION DATA REPLAY

The Persistent Cyber Training Environment (PCTE) has been developed as the joint force solution to provide a single training environment for cyberspace operations. PCTE offers a closed network for Joint Cyberspace Operations Forces, which provides a range of training solutions from individual sustainment training to mission rehearsal and post-operation analysis. Currently, PCTE does not have the ability to replay previously executed training scenarios or external scenarios. Replaying cyber mission data on a digital twin virtual network within PCTE would support operator training as well as enable development and testing of new strategies for offensive and defensive cyberspace operations. A necessary first step in developing such a tool is to acquire network specifications for a target network, or to extract network specifications from a cyber mission data set. This research developed a program design and proof-of-concept tool, Automated Cyber Operations Mission Data Replay (ACOMDR), to extract a portion of the network specifications necessary to instantiate a digital twin network within PCTE from cyber mission data. From this research, we were able to identify key areas for future work to increase the fidelity of the network specification and replay cyber events within PCTE.Captain, United States Marine CorpsApproved for public release. Distribution is unlimited

Baroclinic Vorticity Production in Protoplanetary Disks; Part I: Vortex Formation

The formation of vortices in protoplanetary disks is explored via pseudo-spectral numerical simulations of an anelastic-gas model. This model is a coupled set of equations for vorticity and temperature in two dimensions which includes baroclinic vorticity production and radiative cooling. Vortex formation is unambiguously shown to be caused by baroclinicity because (1) these simulations have zero initial perturbation vorticity and a nonzero initial temperature distribution; and (2) turning off the baroclinic term halts vortex formation, as shown by an immediate drop in kinetic energy and vorticity. Vortex strength increases with: larger background temperature gradients; warmer background temperatures; larger initial temperature perturbations; higher Reynolds number; and higher resolution. In the simulations presented here vortices form when the background temperatures are $\sim 200K$ and vary radially as $r^{-0.25}$, the initial vorticity perturbations are zero, the initial temperature perturbations are 5% of the background, and the Reynolds number is $10^9$. A sensitivity study consisting of 74 simulations showed that as resolution and Reynolds number increase, vortices can form with smaller initial temperature perturbations, lower background temperatures, and smaller background temperature gradients. For the parameter ranges of these simulations, the disk is shown to be convectively stable by the Solberg-H{\o}iland criteria.Comment: Originally submitted to The Astrophysical Journal April 3, 2006; resubmitted November 3, 2006; accepted Dec 5, 200